Perturbative Analysis of Spectral Singularities and Their Optical Realizations

Abstract

We develop a perturbative method of computing spectral singularities of a Schreodinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as an antilaser. We use our general results to establish the exactness of the n-th order perturbation theory for an arbitrary complex potential consisting of n delta-functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.

13 pages, 2 figures, one table, a reference added, typos corrected

References in corpus (6)

• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Coherent Perfect Absorbers: Time-reversed Lasers
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Coherent perfect absorption in a homogeneously-broadened two-level medium
• Delta-Function Potential with a Complex Coupling
• Time-reversed optical parametric oscillation

Cited by in corpus (18)

• Nonlinear Spectral Singularities for Localized Nonlinearities
• Spectral singularities in PT-symmetric periodic finite-gap systems
• Transfer Matrices as Non-Unitary S-Matrices, Multimode Unidirectional Invisibility, and Perturbative Inverse Scattering
• Nonlinear Spectral Singularities and Lasing Threshold Condition
• Spectral Singularities and Whispering Gallery Modes of a Cylindrical Gain Medium
• Generalized Unitarity and Reciprocity Relations for PT-symmetric Scattering Potentials
• Lasing Threshold Condition for Oblique TE and TM Modes, Spectral Singularities, and Coherent Perfect Absorption
• Spectral Singularities in the Surface Modes of a Spherical Gain Medium
• Unitarity corridors to exceptional points
• Spectral Singularities in the TE and TM modes of a PT-Symmetric Slab System: Optimal conditions for realizing a CPA-Laser
• Admissible perturbations and false instabilities in PT-symmetric quantum systems
• Perturbative Unidirectional Invisibility
• Transmission of low-energy scalar waves through a traversable wormhole
• Exact Solution of the Two-Dimensional Scattering Problem for a Class of $\delta$-Function Potentials Supported on Subsets of a Line
• On S-matrix of Schrodinger Operators with Non-Symmetric Zero-Range Potentials
• Hermitian--to--quasi-Hermitian quantum phase transitions
• Scattering Theory and $\mathcal{P}\mathcal{T}$-Symmetry
• Spectral singularity in composite systems and simulation of a resonant lasing cavity